Stuart Lancaster, centre, celebrates after England beat France in the Six Nations. Photograph: David Rogers/Getty Images

England's captain, Chris Robshaw, has urged the Rugby Football Union to give Stuart Lancaster and his fellow coaches its long-term backing following yesterday's record-breaking 24-22 victory in Paris. England have now won three away games in the Six Nations for the first time in their history and lie second in the table behind grand-slam-chasing Wales.

Wales remain short-odds favourites for the title but England once again proved they are a rejuvenated side under Lancaster's stewardship. "We've come a long way in six weeks and I think that's credit to the coaches," Robshaw said. "Stuart and the coaches behind the scenes have been great in terms of creating a great environment and allowing us to play the rugby we want to play. We feel they've given us an opportunity to go out and play. You want to feel you are playing for the coaches as well as each other."

The assistant coach Andy Farrell also believes Lancaster deserves the job permanently. "I think it's there for all to see. The biggest achievement has been to put pride back in the England jersey, not just in the squad but across the whole country. Everyone's at home enjoying the ride with us. It's given us massive belief. We've had some doubters but there's no harder game than Paris away. To play as they did …you can't underestimate how big an achievement that is."

Lancaster preferred to give his players the credit for inflicting France's first home Six Nations defeat in 11 matches. "I've said all along it's not about me, Andy or Graham Rowntree, it's about the team. It epitomised the character we think we've got in the side we're building. We have a huge amount of self-belief in the direction we're going."

England now require France to defeat Wales in Cardiff and then score a hatful of points against Ireland at Twickenham on Saturday to have any hope of sneaking the title but this result will convince many they are heading in the right direction. They scored three excellent tries, including a sensational 71st-minute solo effort from the flanker Tom Croft.

"You can't control the other results," Lancaster said. "All we can focus on is an Irish side we've all got a huge amount of respect for. We'll keep our feet on the ground and make sure we're ready for Saturday. It's my job to get the team ready for Ireland and it should be a great finish to the Six Nations."

Robshaw admitted he feared France might sneak a win in the closing minute through their replacement fly-half François Trinh-Duc. "When that drop-goal was kicked everyone's heart was in their mouths," he said. Rowntree, the only coaching survivor from the World Cup debacle, could barely hide his delight. "A lot of people said a lot of things after the World Cup. I'm exceptionally proud."